| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Construct probability distribution from scenario |
| Difficulty | Moderate -0.8 This is a straightforward probability distribution question requiring systematic enumeration of outcomes from two independent spinners (4×3=12 equally likely outcomes), constructing a table, and applying standard variance formula. It's routine S1 material with no conceptual challenges—purely mechanical execution of basic probability and variance calculations. |
| Spec | 2.04a Discrete probability distributions5.02b Expectation and variance: discrete random variables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Probability distribution table with correct scores with at least one probability | B1 | Table: \(x\): \(-1, 0, 1, 2, 3, 4\); \(P\): \(\frac{1}{12}, \frac{3}{12}, \frac{3}{12}, \frac{2}{12}, \frac{2}{12}, \frac{1}{12}\) |
| At least 4 probabilities correct | B1 | |
| All probabilities correct | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(E(X) = \frac{-1+0+3+4+6+4}{12} = \frac{16}{12} = \frac{4}{3}\) | B1 | |
| \(\text{Var}(X) = \frac{1+0+3+8+18+16}{12} - \left(\frac{4}{3}\right)^2\) | M1 | |
| \(\frac{37}{18}\ (= 2.06)\) | A1 |
## Question 4:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Probability distribution table with correct scores with at least one probability | B1 | Table: $x$: $-1, 0, 1, 2, 3, 4$; $P$: $\frac{1}{12}, \frac{3}{12}, \frac{3}{12}, \frac{2}{12}, \frac{2}{12}, \frac{1}{12}$ |
| At least 4 probabilities correct | B1 | |
| All probabilities correct | B1 | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $E(X) = \frac{-1+0+3+4+6+4}{12} = \frac{16}{12} = \frac{4}{3}$ | B1 | |
| $\text{Var}(X) = \frac{1+0+3+8+18+16}{12} - \left(\frac{4}{3}\right)^2$ | M1 | |
| $\frac{37}{18}\ (= 2.06)$ | A1 | |
---4 A fair four-sided spinner has edges numbered 1, 2, 2, 3. A fair three-sided spinner has edges numbered $- 2 , - 1,1$. Each spinner is spun and the number on the edge on which it comes to rest is noted. The random variable $X$ is the sum of the two numbers that have been noted.
\begin{enumerate}[label=(\alph*)]
\item Draw up the probability distribution table for $X$.
\item Find $\operatorname { Var } ( X )$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2020 Q4 [6]}}